A research blog containing 0th drafts and "open questions" - with a focus on philosophy of math.

Tuesday, February 7, 2012

Kripke's Paderewski and Frege's Common Coin

Maybe this was already obvious to everyone but ...

Kripke's Paderewski example can be modified to refute both the attractive principle Frege's Common Coin, below, and contemporary weakenings of that principle which exempt indexical and demonstrative sentences, or require that all speakers be normally linguistically component.

Frege's Common Coin:a) When two sincere speakers "disagree over" a sentence*, there is a single proposition expressed by this sentence in this context which one believes and the other does not believe,(and indeed believes the negation of).b) When two sincere speakers "agree about" a sentence, there is a single proposition expressed by this sentence in this context which they both believe.

*[I realize this is an awkward locution, but I just mean the intuitive kind of disagreement which occurs when I say "snow is red" and you say "snow isn't red" but doesn't occur when I say "I'm tired" and you say "I'm not tired". It sounds far more natural to say `disagree over a proposition' but we will see that it is actually not clear whether these scenarios involve disagreement over a proposition.]

Consider the following drama involving Pierre, a man in a thought experiment of Kripkie's who knows the musical statesman Paderewski in two different ways, and doesn't realize that Paderewski the pianist is Paderewski the anarchist. Suppose all the following utterances are sincere,Act 1 (musical evening)pierre:"Paderewski is tall" p1alice:"yes, Paderewski is tall" p2Act 2 (on the street)alice:"Paderewski is tall" p3bob:"yes" p4Act 3 (political rally)bob:"Paderewski is tall" p5pierre:"no, he's not!" let p6 be the proposition that Pierre *denies*

Frege's Common Coin tells us that there are propositions p1…pn which speakers express attitudes towards in all the different phases of our play, that p1=p2, p3=p4, p5=p6 and that Pierre believes p1 and does not believe p6.

But this is a very bad thing to say: By the fact that a person like Alice or Bob who has a single grip on Paderewski presumably says the same thing by asserting this sentence on the street vs. at a political rally or a musical evening p2=p3 and p4=p5.By transitivity of identity p1=p6.Thus Pierre believes p1 and does not believe p1. Contradiction.

[If you are worried about the fact that Pierre is unusually ignorant for his society, and hence may not count as "normally linguistically compent" substitute in the name "John". Now cases like the one above will turn out to be so ubiquitous that denying that Pierre, Alice and Bob know enough to have linguistic competency would imply that no one ever has linguistic competency for names.]

Possible Moral: If we want to take propositions to be the objects of belief then, contra Frege's Common Coin, each sentence must be associated with (something like) a class of different propositions which someone could sincerely assert that sentence in virtue of believing.

Oohhh I wondered whether something from that literature is relevant here. Can you say more about what connection you have in mind?

I mean, both cases involve something like attributing a property to an object under one mode of presentation but not another....[as does Frege's Hesperus/Phosphorus case for that matter]:- Pierre believes that Paderewski is a tall under one mode of presentation but not under another, - Ortcutt believes Mayor is a spy under one mode of presentation but not under another.

But it seems (?) that one can handle the Ortcutt case merely by individuating the content of beliefs somewhat finely e.g. by allowing that there are multiple specific objects of belief associated with different modes of presentation, and having any one of these suffices for having a belief de:re about Mayor. (result: Ortcut believes of Mayor that he is a spy and not a spy, Mayor has the property of being believed to be a spy by Ortcut, as well as the proprty of beling believed not to be a spy by Ortcut).

Now each of these beliefs could and would be expressed in conversation very differently "Mayor is a spy" vs. "That guy in the dark is a spy". Thus *it seems to me* that the Ortcutt example alone does not raise problems for Frege's Common Coin, or any version of the idea that when people are arguing over some indexical and demonstrative free sentence there is a single proposition which they are both entertaining.

Anyhow, I have no idea if the above was the connection that you had in mind, but it would be great to hear more.

Ah, okay, I think we're getting into questions of regimentation and logical representation. My take (well, Quine's take) is that quantification of propositions with constants is problematic because substitutivity falls apart in cases like Ortcutt. I take that to be the case here as well: Paderewski-pianist = Paderewski-anarchist, but the substitution of identity in Pierre's belief does not maintain the truth-value of the belief.

I'm not sure if I follow your Ortcutt solution completely, but if I understand correctly, then the problem in your case becomes how an object of belief can be shared between two people. I am thinking of Geach's Hob/Nob witch case here, which I still think to pose deep problems for intensional accounts.

In sum, I'm pretty sure I agree with the thrust of your critique (Common Coin is unworkable), but I think the flaw lies earlier in the case.

Ortcutt motivates us to deny subsitutivity i.e., allowing that beliefs can involve different modes of presentation, such that believing that s is p under one description does not imply believing it under another description. However denying substituitivity does not yet commit one to rejecting the idea that these more finely individuated belief-contents are shared in communication. Thus Pierre shows us something (FCC fails) that mere consideration of Ortcutt does not.

Bearing in mind your "John" point, I figured that the Common Coin defender could claim an implicit indexicality to the Paderewski case such that the non-indexical equivalent would require using different names.

To approach it from a different angle...postulating belief contents that are more finely delineated than sentences themselves seems to beg the question: doesn't that already guarantee the possibility that belief-contents no longer match up? If so, Ortcutt already causes FCC to fail.

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Sometimes the fastest route to getting the right answer is to say something wrong clearly enough. I'm going to try to make a lot of proposals that are initially appealing (but probably ultimately wrong) clearly.

Then (in the comments and elsewhere), I'll try to see exactly where these proposals fail. I hope you will help with the debugging!